In my students' solving of combinatorial tasks, I feel that their being careful and deliberate in their work is an important part of their success. Is there work out there that provides language for such care/attention, and how is being careful measured? I see connections with the Common Core's "attend to precision" standard for mathematical practice, but I'm curious about characterizing this phenomenon from a research perspective.
Thanks for posting this question. I would also be interested to read what is known here. I think I might have seen qualities like "patience" and "attention to detail" in the context of, say, classroom norms ... I don't recall... maybe Cobb and Yackel come to mind? But as an important element of problem solving, I would love to read more research on this.
This is not quite the same thing, but we have a CERME Proceedings paper on Bandura's concept of self-efficiacy as it applies to proving. In addition, I have often noted that my preservice elementary teachers do not work systematically (on a combinatorial problem such as how many different combinations of skirts and blouses can be made with 2 different skirts and 3 different blouses), whereas my math majors (when asked a similar question) do work systematically. This is before they have learned a formula for answering the question.
I know research in Mathematics Education in Spain that is using the concept of flow, an idea from the work of Mihaly Csikszentmihalyi, that is near of intrinsic motivation, and is related to a high level of concentration and engagement with a task, and belongs to affective domain.
You can see a description of the original idea in:
http://www.psy-flow.com/sites/psy-flow/files/docs/flow.pdf
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